Turing's original reaction network is systematically studied, particularly in what concerns: (a) Its ability to produce patterns in a predictable way. (b) The feasibility of its concentration-independent sink term. Despite the widely accepted view that Turing's original model presents some inherent inability to produce regular structures, the pattern formation properties of this model are found to obey the predictions of the corresponding Linear Stability Analysis in the one-dimension and in 'small' two-dimensional systems. An 'Enzymatic' variation of the original Turing's Model is introduced, where the unrealistic sink term is substituted by an enzymatic degradation. It seems that reaction networks of this type can inspire a promising search for chemical or biochemical experimental systems with pattern formation properties, even in the absence of high non-linearities. It is pointed out that temporal oscillations, impossible for the original Turing's Model, are stable and persistent in its Enzymatic variation.